Method of growing a crystal



Dec. 19, 1967 c ARST METHOD OF GROWING A CRYSTAL 3 Sheets-Sheet 1 Filed May 25, 1954 FIG.2.

FIG.

FIG.3.

INVENTOR. MARGRETH C. ARST flW ATTORNEY.

Dec. 19, 1967 Filed May 25, 1964 HEATER TEMPERATURE REQUIRED TO GROW INGOT I M. c. ARST METHOD OF GROWING A CRYSTAL 3 Sheets-Sheet 2 LENGTH OF CRYSTAL HEATER TEMP.

INVENTOR. MARGRETH C ARST DISTANCE FROM TOP OF HEATER ATTORNEY United States Patent 3,359,977 METHUD 0F GROWING A CRYSTAL Margreth C. Arst, Van Nuys, Califi, assignor, by mesne assignments, to Globe-Union Inc, Milwaukee, Wis, a corporation of Delaware Fiied May 25, 1964, Ser. No. 371,874 2 Claims. (Cl. 23301) This application is a continuation-in-part of my copending application, now abandoned, Serial No. 42,823, entitled, Method of Growing a Crystal, filed July 14, 1960, and assigned to the assignee of the present application.

The present invention relates to methods of growing crystals and more particularly to methods utilizing a linear power input to grow crystals in a furnace.

In growing crystals, particularly of semiconductor materials such as silicon, it is the practice to dip a single crystal seed of the material into the same material in a molten state in a crucible. The seed is rotated and withdrawn slowly to produce a single crystal from the molten mass or melt. The temperature of the melt during the crystal growing process is very critical, since the temperature determines the size and shape of the resulting crystal. The temperature of the melt is determined by the temperature of the heater used to heat the melt and the thermodynamic characteristics of the system. During the crystal growing process, it is necessary to vary the temperature of the heater in accordance with the desired configuration of the finished crystal.

Present crystal growing methods known in the art have required that the lowering of the temperature of the heater during the growing of the crystal be accomplished by supplying it input power at several different rates, which is very undesirable because of the extra equipment needed for rate changing, and the difficulty of knowing just when and how much to change the rate. The heating sequence is initiated by heating the silicon until it melts and bringing it to the proper temperature so that when the seed is lowered into the melt the silicon will start to crystallize on the seed. When crystallization starts, the seed is very slowly raised, and the temperature of the heater is slowly decreased, so that the head of the crystal will form. When the proper diameter has been obtained, the radial position of the interface of the melt and the crystal is maintained constant. However, since the volume of the melt remaining in the crucible continually decreases as the crystal volume increases, it is necessary to slowly decrease the temperature of the heater in order to maintain the interface at a constant radial position.

It is an object of the present invention, therefore, to provide a novel method of growing a crystal.

It is another object of the present invention to provide -a novel method of growing a crystal in a furnace without changing the rate at which the power input to the heater decreases once the process starts.

According to the present invention, a method is provided for using a heater having a non-uniform heat loss distribution and locating the crucible containing the melt in such a position with respect to the heater that as the volume of the melt decreases, the top of the melt passes through a temperature gradient, thereby eliminating the need to change the rate at which the power input to the heater decreases.

The features of the present invention which are believed to be novel are set forth with particularity in the appended claims. The present invention, both as to its organization and manner of operation, together with further objects and advantages thereof, may best be understood by reference to the following description, taken in connection with the accompanying drawings, in which:

Patented Dec. E9, 1967 ice FIGURE 1 is a cross-sectional view of a crystal growing furnace that functions in accordance with the method of the present invention.

FIGURE 2 is an isometric view of the heater shown in FIGURE 1.

FIGURE 3 is an isometric view of a complete crystal grown in accordance with the method of the present invention.

FIGURE 4 is a graph of the length of the crystal shown in FIGURE 3 plotted against the heater temperature that is required to grow the ingot.

FIGURE 5 is a graph of the temperature within the heater shown in FIGURE 2 with a constant power input plotted against the distance from the top of the heater.

FIGURE 6 is a graph showing the curves of FIGURES 4 and 5 together with a curve showing the power input to the heater in accordance with the present invention.

FIGURE 7 is a graph of the percent of material left in the crucible plotted against the pulling time.

Referring now to the drawings, FIGURE 1 shows crystal growing furnace 10 having shelf 11 for supporting cylindrical heat insulation 12 and carbon heater 13, and shelf 14 for supporting motor 15 and gear 16. Furnace 10 can be made of stainless steel and insulation 12 and insulation cover 17 can be made of quartz wool. Lever arm 21 is pivotally connected to support 22 by pin 23. Threaded shaft 24 couples arm 21 to support 22 and can be rotated by hand wheel 25. Lever arm 21, support 22, pin 23, threaded shaft 24, and hand wheel 25 can all be made of stainless steel. Carbon crucible holder 30 and quartz crucible 31 containing silicon melt 32 are supported within heater 13 by stainless steel platform 33, which is connected to stainless steel platform shaft 34. End 35 of arm 21 supports shaft 34. Stainless steel chuck 41, which is suspended from the lower end of stainless steel shaft 42, securely grips silicon seed 43. Shaft 42 can be raised or lowered by motor 15 and gear 16.

FIGURE 2 shows carbon heater 13 in greater detail. Heater 13 is cylindrical and slotted with a resistance between ends 44 and 45 of .05 ohms. Heater 13 has an outer diameter of 4 /2 inches, an inner diameter of 3% inches, and a height of 6 inches. The distance between sides 51 and 52 is equal to the distance between sides 53 and 54, namely of an inch, which is less than the distance between corners 55 and 56, because of the geometry of the design. The same relationship holds true for the other sides and corners of heater 13. Electrical resistance is inversely proportional to the crosssectional area of a conductor and the heat loss of a conductor is proportional to its resistance. Consequently, a narrow conductor is subject to greater heat loss than a wide conductor, and the central region of cylindrical heater 13 will be the hottest region when an electrical potential is applied across ends 44 and 45.

FIGURE 3 shows an enlarged view of a complete silicon crystal grown upon seed 43. Head region 61 tapers through shoulder region 62 into body region 63. The operation of the furnace shown in FIGURE 1 will now be described.

Heater 13 is brought to the initial operating temperature, which produces the desired starting temperature at the center of the top surface of melt 32, which is the point where seed 43 will touch the melt when lowered into it. A correct setting of the temperature will cause the molten silicon to start forming into an ingot with the same diameter as seed 43, which in cross-sectional area forms a one-quarter inch square having the desired crystalline orientation. It the temperature is too high, the seed itself will melt and no ingot will form. If the temperature is too low, the contact of solid seed and liquid melt will cause the entire top surface of the liquid to immediately freeze to the seed, ruining the crystal. This temperature is the same no matter where crucible 31 is positioned in the non-uniform temperature zone of heater 13. Different amounts of power are required to maintain this temperature for different positions of crucible 31 within heater 13 and for different quantities of silicon in crucible 31.

The position of crucible 31 within heater 13 is controlled by the rotation of wheel 25 tomove end 35 of arm 21 up or down. Once crucible 31 is properly positioned, gear 16 is rotated to lower shaft 42 until seed 43 makes contact with melt 32 in crucible 31. Melt 32 is allowed to cool slowly until it starts solidifying about seed 43. Shaft 42 is then very slowly and steadily raised vertically. As seed 43 rises vertically, shaft 42 is rotated and melt 32 continues to crystallize'I-Iead and shoulder regions 61 and 62, which form the connection between seed 43 and the desired uniform body region 63, must not be built up too rapidly or else the freezing of melt 32 to the side of crucible 31 or misorientation of the crystalline structure may result. A 45-degree angle for head and shoulder regions 61 and 62 is regarded as optimum.

Body region 63 is built up so as to have a constant diameter by maintaining the heater temperature such that the radial position of the interface between the solid and liquid stays as constant as possible. If the interface position is not held constant, the diameter of the crystal will vary. While this variance is not in itself harmful to the crystal, it is desirable to maintain the conditions described as uniform as possible in order to obtain uniform crystalline structure.

Changes in the diameter of the crystal, therefore, are indicative of non-uniform temperature conditions as the pull progresses and possibly also indicate inferior crystalline structure. This diameter variance occurs because of the temperature gradient between the center of the melt and the edge, which is closer to the heater; the closer to the heater, the higher the temperature. Lowering the temperature at the heater results in a wider diameter crystal being formed, since silicon goes from a liquid to a solid state at only one temperature, and that temperature would then be located closer to the edge of the crucible.

The final step is tipping out, which is the recovery of the material left in the crucible when there is too little remaining to provide the proper conditions for crystal formation. By properly shaping the bottom of crucible 31, this tipping out can be minimized.

Furnace 10 must be constructed so as to provide the optimum conditions for uniform crystal growth. The first construction consideration is the avoidance of sudden temperature changes in the melt, which can be caused by changes in the control equipment or by outside power fluctuations. Automatic-pull control equipment capable of producing a linear temperature decrease helps eliminate such changes in the control equipment, and the use of a well-sealed heat chamber, in addition to the use of a temperature element having a fast response, helps eliminate rapid changes caused by outside power fluctuations. Sudden temperature changes and thermal shock can cause twinning and increase dislocation density.

Vibration must be eliminated as completely as possible, as by mounting all motors on special shock mountings. The shafts should be guided by precision bearings and should be perfectly balanced. The connections of these components to the furnace should be made, whereever possible, by vibration-free means. The furnace itself should be mounted on a special slab to insulate it from vibrations of nearby equipment. Changes in the temperature balance of the furnace should also be avoided. If water is used to cool the furnace, the cooling water should flow smoothly and under constant pressure through the cooling areas in the stainless steel cylinder and in the cooling areas around the bearings, the purpose being to avoid vibrations or heat balance changes. Changes in the flow of the cooling fluid could cause a shaft to bind or a change in the rate of heat removal.

An optimum temperature control system would measure the temperature of the melt at the desired position of the interface and would hold it as constant as possible. Since that is a practical impossibility, the method of the present invention uses indirect measurements that are controlled only through a relative relationship.

The temperature sensing element in this control system is a sapphire rod that is set to measure the temperature near the bottom of the crucible holder, which is heated by the heater and acts as a heater itself by transmitting its own heat into the silicon melt. The temperature of the crucible holder will have to decrease as the amount of silicon in the crucible decreases and the heat losses and temperature gradient across the melt decrease. The automatic programmer of the present temperature control system decreases the temperature of the crucible holder at a predetermined rate so as to maintain constant the position of the interface of the crystal and the melt.

The programmer can be set by means of adjustable gears to provide one-half, one, or two hour linear temperature changes between the present limits of the instrument. The use of a one-hour gear would decrease the temperature from the maximum to the minimum of the preset operating range in one hour. The time can be adjusted into other rates by means of an external rate adjustment control, which if set at 50% will increase the present time to two hours, and if set at 25% will increase the preset time to four hours, etc. The only requirement for the initial setup is that the scale must be greater than the desired program, so that an automatic pull may be made from the head to the tipping out state without running off the scale of the instrument.

FIGURE 4 shows a graph of the heater temperature changes through which the top surface of the melt would have to pass for an ingot pull in an absolutely uniform and heat tight system. Curve 71, having a slope of the angle 0: represents the temperature drop when growing the head of the ingot at approximately 45. When seed 43 is lowered into melt 32, the temperature of melt 32 varies from about 1420 C. at the center of the surface of melt 32 to about 1430 C. at the periphery. When the silicon starts solidifying upon seed 43, motor 15 starts raising seed 43, and the temperature of the heater is required to fall at a constant rate to move the interface radially outward and thereby build the head of the crystal, as shown by curve portion 71. As long as this rate remains constant, shoulder region 62 is formed and the diameter of the crystal increases. When the desired diameter is obtained, it becomes necessary to keep the radial position of the interface constant since body region 63 will grow straight as long as the interface position remains constant.

The difficulty is that as the crystal diameter grows larger, the volume of the silicon remaining in the melt decreases and the heat losses, primarily from radiation, also decrease. In order to maintain the position of the interface constant, it becomes necessary to decrease the temperature of heater 13 at a constant rate, as shown by curve portion 72, which has a slope of the angle 0: This can be accomplished by decreasing the power to heater 13 at a rate to cause the heater temperature to change such that the interface in the diminishing amount of material in crucible 31 is maintained at the desired radial position. The problem is to avoid the necessity of changing the rate at which the temperature of heater 13,

and consequently the power thereto, is required to decrease. Bottom region 73 can be any shape that results when all the melt is used up, which will occur after three hours and 50 minutes for a pull speed of .0003 inch per second if 500 grams of melt is used and the crystal body portion is about two inches in diameter.

FIGURE 5 shows a graph of the temperature of heater 13 at a given power input plotted against the distance from its top. Curve portions 74 and 75 show that the top and bottom portions of heater 13 are the coolest and have increasing and decreasing temperature gradients respectively, and curve portion 76 shows that the temperature is constant over the mid-region of heater 13. This kind of temperature characteristic is present in types of heaters other than the slotted heater shown in FIG- URE 2 and, for example, the common spiral heater could be used.

FIGURE 6 shows the result of using a heater having a temperature characteristic of the nature shown in FIG- URE 5 to achieve the desired heater temperature characteristic curve of FIGURE 4. As can be seen, the use of such a heater permits the power input to the heater to be reduced at a constant rate while producing temperature conditions in the melt that approximate the conditions that would be present if the power input to a heater having a uniform temperature characteristic was reduced at two different rates to produce the heater temperature curves 71, 78. A uniformly reproducible ingot can thus be produced by setting a single linear temperature rate of decrease for the complete pull at the same angle a that is required-to produce the heater temperature curve 78.

By properly locating crucible 31 within heater 13 it becomes possible to take advantage of the temperature gradient produced within melt 32 and to avoid the necessity of changing the rate of temperature decrease of heater 13. Since the body portion will start to grow at the point where the constant temperature portion of the heater begins, the crucible should be positioned such that the desired diameter is reached at this time. For the 500 grams of silicon shown by way of example in FIGURE 1, and when a l /z-inch diameter crystal is to be grown, the surface of melt 32 should be approximately level with the top of heater 13. If less silicon is used, or a crystal with a larger diameter is desired, crucible 31 must be raised, and if more silicon is used, or a smaller diameter crystal is desired, crucible 31 must be lowered. During the crystal growing period, as the size of the crystal increases and the level of melt 32 drops, the top of the melt moves through the temperature gradient present within heater 13 and crucible 31. Thus, by proper placement of crucible 31 within the heater 13, the heater temperature characteristic as seen by the melt can be made to closely approximate the desired form shown in FIGURE 4. For the quantities of materials used by way of example, it has been found desirable to linearly decrease the electric current passed through heater 13 from 470 amperes at the beginning of the crystal growing process to 430 amperes at the end.

A mathematical approximation for a pull will now be described.

and

=M/X where X equals the amount of silicon pulled per second, in

grams d equals the diameter of the ingot, in centimeters S equals the pull speed, in centimeters per second r equals the time in seconds, and

M equals the amount of silicon in the melt, in grams reduction rate necessary to maintain the radial position of the interface of the melt and the crystal constant during the entire pull.

Since the temperature cannot be measured directly at the interface, the heat balance characteristics of the furnace system must be determined under two conditions. One condition, F, occurs when the seed is dipped into the melt and the crucible is filled with a given amount, M, of material, the top surface of which is at the starting temperature, T, and the other condition, E, occurs when the crucible is empty and at the temperature that would cause the last drop of silicon left in the crucible at the end of the pull to be formed onto the crystal.

It is apparent that more power will be necessary to maintain condition F than condition E. The power required to achieve condition F must be decreased at the same rate that the material is being removed, so that the power will be equal to the steady state requirement of condition E at the instant that the last part of the crystal is formed. The faster the rate of material removal, the greater the rate of power reduction necessary to achieve the goal of absolute uniformity of the ingot along its entire length. Since other furnaces will have heat balance characteristics of their own, no absolute determination of machine settings can be made. The following calculation will concern itself with relative values only.

By setting the upper limit on the automatic temperature control to the heat necessary to achieve condition F, the power drop can be programmed to coincide with the desired material removal rate. This upper limit will have to be redetermined whenever a change is made in the furnace setup, such as when the amount of material or the pull speed is changed.

FIGURE 7 shows the percent of material left in the crucible plotted against the pulling time. The relative rates of power reduction are shown as the slopes of the lines formed by different rates of removal of material while going from condition F to condition E. The slope can be expressed as the tangent of the angle alpha, which is the reciprocal of the time in hours. The angle alpha can be used as the percentage-of-power-reduction setting on the furnace controller directly, if the one-hour gears are in use, as the reduction will then be expressed as a rate per hour in the same manner as the material being removed, which is also at a rate per hour. External adjustments for other gear ratios can easily be determined from the preceding by using the following equations, where 1' equals the time required to pull the entire ingot in hours:

and a crystal with a certain resistivity will be required. Solving for the tangent of alpha,

Then, Where P is the power drop percentage set on the external adjustment control of the automatic temperature control for a given gear ratio,

tan a When the furnace controls are set for the calculated value of P, and the crucible is correctly positioned in the heater, the head will be automatically formed, and the shoulder will grow out to the desired diameter to form a perfectly shaped ingot. Since the temperature drop of the heater is calculated for a crystal having a diameter much larger than that of the seed, when the smaller diameter parts of the head are formed, the rate of material removal will be much slower than during the main part of the pull. Ordinarily, the temperature drop would be so rapid as to cause the head to form too rapidly and would produce an inferior crystal. This drop is counter balanced by the heater configuration which causes the heater temperature to vary along the length of the heater. A proper positioning of the crucible in the heater balances these two forces and causes the head to form until the cutoff point is reached.

By such an arrangement, the desired diameter is built up when the cutofi point is reached, and, since the cutoff point occurs at the location in the heater where the constant temperature zone starts, the crystal will stop increasing in diameter. Instead, the constant diameter portion of its growth will start, with material being removed at the same rate that the power is being reduced. Thus, given values for all of the variables of the system, a uniformly reproducible crystal may be consistently pulled with one linear power setting. Such a crystal will have an optimum crystalline structure with a minimum of dislocations.

While particular embodiments of the present invention have been shown and described, it will be obvious to those skilled in the art that changes and modifications may be made without departing from this invention in its broader aspects, and, therefore, the aim in the appended claims is to cover all such changes and modifications as fall within the true spirit and scope of this invention.

I claim:

1. A method of growing a crystal of an element selected from the group consisting of silicon and germanium, comprising the steps of: placing a crucible containing a melt of said element within a heater having an increasing temperature gradient region and a contiguous constant temperature region, positioning said crucible so that the upper portion of said melt is in said increasing temperature gradient region of said heater and the lower portion of said melt is in said constant temperature region of said heater, placing a crystal-growing seed in contact with the upper surface of said melt, and decreasing the power input to said heater at a constant rate while slowly withdrawing said seed from said melt at a constant rate so that a single crystal having head, sloping shoulder, and straight body regions is grown onto said seed without either of said rates being changed.

2. The method of claim 1 wherein said heater is a substantially cylindrical electrical heater.

References Cited UNITED STATES PATENTS 2,768,914 10/1956 Buehler.

2,851,342 9/1958 Bradshaw et a1. 23-301 2,852,420 9/1958 Pohl.

2,975,036 3/1961 Taylor et al. 23301 X OTHER REFERENCES Marshall et al., Journal of Scientific Instruments, vol. 35, April 1958, pages 121-125.

Hannay, Semiconductors, Feb. 27, 1959, Reinhold Publishing Co., pages 101-110.

NORMAN YUDKOFF, Primary Examiner.

G. D. MITCHELL, Examiner. G. HINES, A. J. ADAMCIK, Assistant Examiners. 

1. A METHOD OF GROWING A CRYSTAL OF AN ELEMENT SELECTED FROM THE GROUP CONSISTING OF SILICON AND GERMANIUM, COMPRISING THE STEPS OF: PLACING A CRUCIBLE CONTAINING A MELT OF SAID ELEMENT WITHIN A HEATER HAVING AN INCREASING TEMPERATURE GRADIENT REGION AND A CONTIGUOUS CONSTANT TEMPERATURE REGION, POSITIONING SAID CRUCIBLE SO THAT THE UPPER PORTION OF SAID MELT IS IN SAID INCREASING TEMPERATURE GRADIENT REGION OF SAID HEATER AND THE LOWER PORTION OF SAID MELT IS IN SAID CONSTANT TEMPERATURE REGION OF SAID HEATER, PLACING A CRYSTAL-GROWING SEED IN CONTACT WITH THE UPPER SURFACE OF SAID MELT, AND DECREASING THE POWER INPUT TO SAID HEATER AT A CONSTANT RATE WHILE SLOWLY WITHDRAWING SAID SEED FROM SAID MELT AT A CONSTANT RATE SO THAT A SINGLE CRYSTAL HAVING HEAD, SLOPING SHOULDER, AND STRAIGHT 